A least-squares virtual element method on polytopal mesh for a curl-div system.
Saved in:
| Title: | A least-squares virtual element method on polytopal mesh for a curl-div system. |
|---|---|
| Authors: | Duan, Huoyuan1 (AUTHOR) hyduan.math@whu.edu.cn, Zhu, Duowei1,2 (AUTHOR) dwzhu.cherry@whu.edu.cn |
| Source: | Journal of Computational & Applied Mathematics. Aug2026, Vol. 481, pN.PAG-N.PAG. 1p. |
| Subjects: | Magnetostatics, Least squares, Polytopes, Finite element method, Numerical calculations, Error analysis in mathematics, Orthogonal decompositions |
| Abstract: | A new virtual element method of least-squares type is proposed for numerically solving a curl-div system, which typically arises from the magnetostatic problem. We employ the nodal virtual elements on polytopal meshes. With the Helmholtz L 2-orthogonal decomposition and the related regular-singular decomposition, we develop a rigorous argument for proving the L 2-coercivity. For the k (k ≥ 1) order virtual element which has the degrees of freedom in the interiors of the element faces, we strictly establish the optimal error estimates O (hr) for the singular solution which has a low regularity and only belongs to (Hr (Ω)) d , d = 2 , 3 , for 1/2 < r < 1. For higher-order regularity solution, L 2-norm O (h k + 1) optimal convergence can hold for k ≥ 1. Numerical results are provided. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
Be the first to leave a comment!
